Operations with Signed Rational Numbers: Additional Practice (Set 2)

The signs differ, so the quotient is negative. Write $0.4 = \tfrac{2}{5}$ and multiply by its reciprocal.

$\frac{4}{5} \times \frac{5}{2} = \frac{20}{10} = 2$

So the quotient is $-2$. The choice $-0.32$ multiplies instead of dividing.

The fraction $\tfrac{3}{8}$ ends as a decimal, $0.375$, so the decimal form works here. The signs differ, so subtract the smaller size from the larger.

$1.600 - 0.375 = 1.225$

The number $-1.6$ is farther from zero, so the answer is $-1.225$.

The signs differ, so the product is negative. Write $0.6 = \tfrac{3}{5}$ for the size.

$\frac{5}{9} \times \frac{3}{5} = \frac{15}{45} = \frac{1}{3}$

So the product is $-\tfrac{1}{3}$. The choice $-\tfrac{25}{27}$ divides instead of multiplying.

The change is the new reading minus the old one, and subtracting is adding the opposite.

$-3.5 - 1.25 = -3.5 + (-1.25) = -4.75$

The change is negative because the temperature fell: $1.25$ degrees down to zero, and $3.5$ more below it.

Write $0.4 = \tfrac{2}{5}$ and compare the sizes over thirtieths.

$\frac{1}{3} = \frac{10}{30} < \frac{2}{5} = \frac{12}{30} < \frac{1}{2} = \frac{15}{30}$

So $-\tfrac{1}{2} < -0.4 < -\tfrac{1}{3}$. The size $0.3$ is below $\tfrac{1}{3}$, and $0.55$ and $0.6$ are above $\tfrac{1}{2}$.

The bars group, so work out the inside first. Over sixths it is $-\tfrac{4}{6} + \left(-\tfrac{1}{6}\right)$, two negatives.

$-\frac{4}{6} - \frac{1}{6} = -\frac{5}{6}$

The absolute value is the distance from zero, so the answer is $\tfrac{5}{6}$.

Write the decimal as a fraction: $-0.125 = -\tfrac{125}{1000} = -\tfrac{1}{8}$. Its reciprocal keeps the minus sign.

$\left(-\frac{1}{8}\right) \times (-8) = 1$

So the reciprocal is $-8$.

Divide in order from the left. The first quotient has matching signs, so it is positive: $\tfrac{1}{2} \times 4 = 2$.

$2 \div (-2) = -1$

The choice $-4$ comes from dividing the last two numbers first, which the order of operations does not allow.

The debt is a balance of $-12.6$ dollars. Paying back a third of it adds $12.6 \div 3 = 4.2$ dollars.

$-12.6 + 4.2 = -8.4$

You still owe two thirds of the debt, $8.4$ dollars, so the balance is $-8.4$ dollars.

No factor is zero. Three of the four factors are negative, an odd count, so the product is negative.

$\frac{1}{2} \times \frac{1}{3} \times 2.4 \times \frac{7}{8} = 0.4 \times \frac{7}{8} = 0.35$

Here $\tfrac{1}{6} \times 2.4 = 0.4$, and $0.4 \times \tfrac{7}{8} = \tfrac{2.8}{8} = 0.35$. So the product is $-0.35$.

The minus sign belongs to the whole mixed number, so $-1\tfrac{2}{5} = -\left(1 + \tfrac{2}{5}\right) = -\tfrac{7}{5} = -1.4$, and $\frac{7}{-5}$ is the same number.

$-1 + \frac{2}{5} = -\frac{3}{5}$

That is a different number, four fifths of a unit to the right of $-1\tfrac{2}{5}$.

Work from the left. A product with a zero factor is zero, so $(-3.6) \times 0 = 0$.

$0 \div (-1.2) = 0$

Zero divided by a nonzero number is zero. Nothing here divides by zero, so the expression is defined.